Mr Tim Davis

Profile

Tim is a final year PhD student who's research area is number theory. The specific area of interest is automorphic forms researching them both from a classical and adelic viewpoint. His supervisor is Prof Abhishek Saha and his PhD is funded through the Leverhulme Trust.

Before starting his PhD he studied at the University of Reading and received his MMath in 2019.

Tim is jointly one of the PhD representatives.

Teaching

Spring 2023

• Introduction to Algebra (TA)

Autumn 2022

• Numbers, Sets and Functions (TA)
• Number Theory (Marking)

Spring 2022

• Introduction to Algebra (TA)

Autumn 2021

• Numbers, Sets and Functions (TA)
• Number Theory (Marking)

Spring 2021

• Introduction to Algebra (TA)

Autumn 2020

• Linear Algebra 1 (TA)
• Number Theory (Marking)

Spring 2020

• Number Theory (Demonstrator & Marking)
• Differential and Integral Analysis (Demonstrator & Marking)

Research

Research Interests:

• Classical and higher rank modular forms
• Representations of p-adic groups
• Algebraic number theory

Tim's research is focused on answering questions about the Fourier coefficients of classical modular forms and other families of modular forms. His current work is investigating the p-adic valuation of Fourier coefficients of classical modular forms. He has previously worked on studying some algebraic properties of the Fourier coefficients of Hilbert modular forms. 

Publications

• Fourier coefficients of Hilbert modular forms at cusps, The Ramanujan Journal (2023), DOI 10.1007/s11139-023-00703-7
• p-adic Valuations of Local Whittaker newforms, in preparation